Entropy Stable Schemes For Relativistic Hydrodynamics Equations

Abstract: In this work, we propose high order finite difference schemes for the equations of relativistic hydrodynamics, which are entropy stable. The crucial components of these schemes are a computationally efficient entropy conservative flux and suitable high order entropy dissipative operators.

We first design a higher order entropy conservative flux. For the construction of appropriate entropy dissipative operators, we derive entropy scaled right eigenvectors. This is then used with ENO based sign preserving reconstruction of scaled entropy variables, which results in higher order entropy stable schemes. Several numerical results are presented up to fourth order to demonstrate entropy stability and performance of these schemes. This is a joint work with Mr. Deepak Bhoriya.